Prior art cable-stripping tools have first and second parts which can rotate relative to one another about an axis and of which a first part carries a cutting blade in the vicinity of the axis and a second part carries a hook which can move axially and which is biased toward an end position relative to the cutting blade by a spring element. The hook has a concave side which faces toward the cutting blade and which functions to receive the cable to be stripped, and also includes a generally axially oriented stem with which the hook is connected to the tool. The cutting blade forms a helical or spiral slit in the cable.